Which of the following numbers is a multiple of 4? ${46,49,65,104,111}$
Answer: The multiples of $4$ are $4$ $8$ $12$ $16$ ..... In general, any number that leaves no remainder when divided by $4$ is considered a multiple of $4$ We can start by dividing each of our answer choices by $4$ $46 \div 4 = 11\text{ R }2$ $49 \div 4 = 12\text{ R }1$ $65 \div 4 = 16\text{ R }1$ $104 \div 4 = 26$ $111 \div 4 = 27\text{ R }3$ The only answer choice that leaves no remainder after the division is $104$ $ 26$ $4$ $104$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $104$ $104 = 2\times2\times2\times13 4 = 2\times2$ Therefore the only multiple of $4$ out of our choices is $104$. We can say that $104$ is divisible by $4$.